Validation of an Original Mathematical Model of CO2 Elimination and Dead Space Ventilation

Validation of at-the-bedside formulae for estimating ventilator driving pressure during airway pressure release ventilation using computer simulation

BACKGROUND

Airway pressure release ventilation (APRV) is widely available on mechanical ventilators and has been proposed as an early intervention to prevent lung injury or as a rescue therapy in the management of refractory hypoxemia. Driving pressure ([Formula: see text]) has been identified in numerous studies as a key indicator of ventilator-induced-lung-injury that needs to be carefully controlled. [Formula: see text] delivered by the ventilator in APRV is not directly measurable in dynamic conditions, and there is no "gold standard" method for its estimation.

METHODS

We used a computational simulator matched to data from 90 patients with acute respiratory distress syndrome (ARDS) to evaluate the accuracy of three "at-the-bedside" methods for estimating ventilator [Formula: see text] during APRV.

RESULTS

Levels of [Formula: see text] delivered by the ventilator in APRV were generally within safe limits, but in some cases exceeded levels specified by protective ventilation strategies. A formula based on estimating the intrinsic positive end expiratory pressure present at the end of the APRV release provided the most accurate estimates of [Formula: see text]. A second formula based on assuming that expiratory flow, volume and pressure decay mono-exponentially, and a third method that requires temporarily switching to volume-controlled ventilation, also provided accurate estimates of true [Formula: see text].

CONCLUSIONS

Levels of [Formula: see text] delivered by the ventilator during APRV can potentially exceed levels specified by standard protective ventilation strategies, highlighting the need for careful monitoring. Our results show that [Formula: see text] delivered by the ventilator during APRV can be accurately estimated at the bedside using simple formulae that are based on readily available measurements.

Hemodynamic effects of lung recruitment maneuvers in acute respiratory distress syndrome

BACKGROUND

Clinical trials have, so far, failed to establish clear beneficial outcomes of recruitment maneuvers (RMs) on patient mortality in acute respiratory distress syndrome (ARDS), and the effects of RMs on the cardiovascular system remain poorly understood.

METHODS

A computational model with highly integrated pulmonary and cardiovascular systems was configured to replicate static and dynamic cardio-pulmonary data from clinical trials. Recruitment maneuvers (RMs) were executed in 23 individual in-silico patients with varying levels of ARDS severity and initial cardiac output. Multiple clinical variables were recorded and analyzed, including arterial oxygenation, cardiac output, peripheral oxygen delivery and alveolar strain.

RESULTS

The maximal recruitment strategy (MRS) maneuver, which implements gradual increments of positive end expiratory pressure (PEEP) followed by PEEP titration, produced improvements in PF ratio, carbon dioxide elimination and dynamic strain in all 23 in-silico patients considered. Reduced cardiac output in the moderate and mild in silico ARDS patients produced significant drops in oxygen delivery during the RM (average decrease of 423 ml min^-1 and 526 ml min^-1, respectively). In the in-silico patients with severe ARDS, however, significantly improved gas-exchange led to an average increase of 89 ml min^-1 in oxygen delivery during the RM, despite a simultaneous fall in cardiac output of more than 3 l min^-1 on average. Post RM increases in oxygen delivery were observed only for the in silico patients with severe ARDS. In patients with high baseline cardiac outputs (>6.5 l min^-1), oxygen delivery never fell below 700 ml min^-1.

CONCLUSIONS

Our results support the hypothesis that patients with severe ARDS and significant numbers of alveolar units available for recruitment may benefit more from RMs. Our results also indicate that a higher than normal initial cardiac output may provide protection against the potentially negative effects of high intrathoracic pressures associated with RMs on cardiac function. Results from in silico patients with mild or moderate ARDS suggest that the detrimental effects of RMs on cardiac output can potentially outweigh the positive effects of alveolar recruitment on oxygenation, resulting in overall reductions in tissue oxygen delivery.

High PEEP in acute respiratory distress syndrome: quantitative evaluation between improved arterial oxygenation and decreased oxygen delivery

BACKGROUND

Positive end-expiratory pressure (PEEP) is widely used to improve oxygenation and prevent alveolar collapse in mechanically ventilated patients with the acute respiratory distress syndrome (ARDS). Although PEEP improves arterial oxygenation predictably, high-PEEP strategies have demonstrated equivocal improvements in ARDS-related mortality. The effect of PEEP on tissue oxygen delivery is poorly understood and is difficult to quantify or investigate in the clinical environment.

METHODS

We investigated the effects of PEEP on tissue oxygen delivery in ARDS using a new, high-fidelity, computational model with highly integrated respiratory and cardiovascular systems. The model was configured to replicate published clinical trial data on the responses of 12 individual ARDS patients to changes in PEEP. These virtual patients were subjected to increasing PEEP levels during a lung-protective ventilation strategy (0-20 cm H₂O). Measured variables included arterial oxygenation, cardiac output, peripheral oxygen delivery, and alveolar strain.

RESULTS

As PEEP increased, tissue oxygen delivery decreased in all subjects (mean reduction of 25% at 20 cm H₂O PEEP), despite an increase in arterial oxygen tension (mean increase 6.7 kPa at 20 cm H₂O PEEP). Changes in arterial oxygenation and tissue oxygen delivery differed between subjects but showed a consistent pattern. Static and dynamic alveolar strain decreased in all patients as PEEP increased.

CONCLUSIONS

Incremental PEEP in ARDS appears to protect alveoli and improve arterial oxygenation, but also appears to impair tissue oxygen delivery significantly because of reduced cardiac output. We propose that this trade-off may explain the poor improvements in mortality associated with high-PEEP ventilation strategies.

Evaluation of the physiological properties of ventilatory ratio in a computational cardiopulmonary model and its clinical application in an acute respiratory distress syndrome population

BACKGROUND

Owing to complexities of measuring dead space, ventilatory failure is difficult to quantify in critical care. A simple, novel index called ventilatory ratio (VR) can quantify ventilatory efficiency at the bedside. The study objectives were to evaluate physiological properties of VR and examine its clinical applicability in acute respiratory distress syndrome (ARDS) patients.

METHODS

A validated computational model of cardiopulmonary physiology [Nottingham Physiology Simulator (NPS)] was used to evaluate VR ex vivo in three virtual patients with varying degrees of gas exchange defects. Arterial P(CO₂) and mixed expired P(CO₂) were obtained from the simulator while either dead space or CO₂ production was altered in isolation. VR and deadspace fraction was calculated using these values. A retrospective analysis of a previously presented prospective ARDS database was then used to evaluate the clinical utility of VR. Basic characteristics of VR and its association with mortality were examined.

RESULTS

The NPS showed that VR behaved in an intuitive manner as would be predicted by its physiological properties. When CO₂ production was constant, there was strong positive correlation between dead space and VR (modified Pearson's r 0.98, P<0.01). The ARDS database had a mean VR of 1.47 (standard deviation 0.58). Non-survivors had a significantly higher VR compared with survivors [1.70 vs 1.34, mean difference 0.35, 95% confidence interval (CI) 0.16-0.56, P<0.01]. VR was an independent predictor of mortality (odds ratio 3.05, CI 1.35-6.91, P<0.01).

CONCLUSIONS

VR is influenced by dead space and CO₂ production. In ARDS, high VR was associated with increased mortality.

Optimization of mechanical ventilator settings for pulmonary disease states

The selection of mechanical ventilator settings that ensure adequate oxygenation and carbon dioxide clearance while minimizing the risk of ventilator-associated lung injury (VALI) is a significant challenge for intensive-care clinicians. Current guidelines are largely based on previous experience combined with recommendations from a limited number of in vivo studies whose data are typically more applicable to populations than to individuals suffering from particular diseases of the lung. By combining validated computational models of pulmonary pathophysiology with global optimization algorithms, we generate in silico experiments to examine current practice and uncover optimal combinations of ventilator settings for individual patient and disease states. Formulating the problem as a multiobjective, multivariable constrained optimization problem, we compute settings of tidal volume, ventilation rate, inspiratory/expiratory ratio, positive end-expiratory pressure and inspired fraction of oxygen that optimally manage the tradeoffs between ensuring adequate oxygenation and carbon dioxide clearance and minimizing the risk of VALI for different pulmonary disease scenarios.

Validation and application of a high-fidelity, computational model of acute respiratory distress syndrome to the examination of the indices of oxygenation at constant lung-state

BACKGROUND

Calculated venous admixture (Qs/Qt) is considered the best index of oxygenation; surrogates have been developed (Pa(O(2))/Fi(O(2)), respiratory index, and arterioalveolar PO(2) difference), but these vary with Fi(O(2)), falsely indicating a change in lung-state. Using a novel model, we aimed to quantify the behaviour of the indices of oxygenation listed above during physiological and treatment factor variation. The study is the first step in developing an accurate and non-invasive tool to quantify oxygenation defects.

METHODS

We present the static and dynamic validation of a novel computational model of gas exchange in acute respiratory distress syndrome (ARDS) based upon the Nottingham Physiology Simulator. Arterial gas tension predictions were compared with data derived from ARDS patients. The subsequent study examined the indices' susceptibility to variation induced by independent changes in Fi(O(2)) (0.3-1.0), haemoglobin concentration (Hb: 6-14 g dl(-1)), oxygen consumption (VO(2): 250-350 ml min(-1)), and Pa(CO(2)) (4-8 kPa).

RESULTS

Static validation produced a mean error of -0.3%, a 10-fold improvement over previous models. Dynamic validation produced a mean prediction error of -0.05 kPa for Pa(O(2)) and 0.09 kPa for Pa(CO(2)). Every parameter, especially Fi(O(2)), induced variation in all indices. The least Fi(O(2))-dependent index was Qs/Qt (variation: 5.1%). In contrast, Pa(O(2))/Fi(O(2)) varied by 77% through the range of Fi(O(2)).

CONCLUSIONS

We have improved simulation of gas exchange in ARDS by using a sophisticated respiratory model. Using the validated model, we have demonstrated that the current indices of oxygenation vary with alteration in Hb, Pa(CO(2)), and VO(2) in addition to their previously well-documented dependence on Fi(O(2)).

Monitoring oxygen transport and tissue oxygenation

PURPOSE OF REVIEW

To review recent publications in the field of oxygen delivery and tissue oxygenation. With few exceptions, we restricted our selection to clinical studies published in the English literature.

RECENT FINDINGS

No major breakthroughs have occurred in the past decade in the diagnosis or treatment of tissue hypoxia. There is renewed interest in goal-directed resuscitation when applied early in the course of treatment. Monitoring metabolic markers of tissue hypoxia continues to hold great clinical interest, in particular, tissue PCO2, near infrared spectroscopy, base deficit and blood lactate concentration. Technical issues, however, seem to restrict the widespread use of many of these techniques.

SUMMARY

There is an urgent need to develop methods to accurately and rapidly identify patients with tissue hypoxia. Perhaps the combination of gastric tonometry, near-infrared spectroscopy, urinary PO2 and continuous measures of mixed (or central) venous O2 saturation may provide the answer. An even more formidable task is that of developing effective therapy to correct tissue hypoxia while avoiding harm to the patient.

Effects of alveolar dead-space, shunt andV˙/Q˙distribution on respiratory dead-space measurements

BACKGROUND

Respiratory dead-space is often increased in lung disease. This study evaluates the effects of increased alveolar dead-space (Vd(alv)), pulmonary shunt, and abnormal ventilation perfusion ratio (/) distributions on dead-space and alveolar partial pressure of carbon dioxide (Pa(co(2))) calculated by various methods, assesses a recently published non-invasive method (Koulouris method) for the measurement of Bohr dead-space, and evaluates an equation for calculating physiological dead-space (Vd(phys)) in the presence of pulmonary shunt.

METHODS

Pulmonary shunt, / distribution and Vd(alv) were varied in a tidally breathing cardiorespiratory model. Respiratory data generated by the model were analysed to calculate dead-spaces by the Fowler, Bohr, Bohr-Enghoff and Koulouris methods. Pa(co(2)) was calculated by the method of Koulouris.

RESULTS

When Vd(alv) is increased, Vd(phys) can be recovered by the Bohr and Bohr-Enghoff equations, but not by the Koulouris method. Shunt increases the calculated Bohr-Enghoff dead-space, but does not affect Fowler, Bohr or Koulouris dead-spaces, or Vd(phys) estimated by the shunt-corrected equation if pulmonary artery catheterization is available. Bohr-Enghoff but not Koulouris or Fowler dead-space increases with increasing severity of / maldistribution. When alveolar Pco(2) is increased by any mechanism, Pa(co(2)) calculated by Koulouris' method does not agree well with average alveolar Pco(2).

CONCLUSIONS

Our studies show that increased pulmonary shunt causes an apparent increase in Vd(phys), and that abnormal / distributions affect the calculated Vd(phys) and Vd(alv), but not Fowler dead-space. Dead-space and Pa(co(2)) calculated by the Koulouris method do not represent true Bohr dead-space and Pa(co(2)) respectively, but the shunt-corrected equation performs well.

The dependence of measured alveolar deadspace on anatomical deadspace volume

BACKGROUND

Changes in pulmonary deadspace are indicators of disease status (e.g. pulmonary embolus, acute respiratory distress syndrome) and they have prognostic usefulness in the intensive care unit. The components of pulmonary deadspace, the alveolar and anatomical deadspaces (VDalv and VDanat), are commonly considered to be independent (i.e. the addition of airway equipment should not alter the measured VDalv). However, VDanat has been shown to affect VDalv in the absence of changes in alveolar ventilation or perfusion. We sought to quantify the variability in measured VDalv induced by changes in VDanat using a cardiorespiratory computational model.

METHODS

Using the Nottingham Physiology Simulator, we examined three simulated ventilated patients with small, moderate and large ventilation-perfusion (VQ) defects. Each patient received 12.5 bpm x 500 ml. We varied VDanat between 50 and 250 ml, keeping the VQ ratio of each alveolus constant. We calculated VDalv by subtracting VDanat (measured using Fowler's technique) from the physiological deadspace (measured using the Bohr-Enghoff equation). We calculated fresh-gas tidal volume (VTfresh) by subtracting VDanat from the exhaled tidal volume and calculated VDalv/VTfresh. In the simulated patient with the large VQ defect, we performed the same protocol with tidal volumes of 750 and 1000 ml.

RESULTS

When VDanat increased from 50 to 250 ml (500 ml tidal volume) VDalv decreased by 48.3% (mean value across the three VQ defects) and VDalv/VTfresh decreased by 15.1%. These relationships were similar at each tidal volume studied.

CONCLUSIONS

Measured VDalv is altered by changes in VDanat despite constant VQ ratios in each alveolus. This has implications for the interpretation of deadspace measured in the clinical setting. The variability is less for the ratio VDalv/VTfresh.

Estimating alveolar dead space from the arterial to end-tidal CO(2) gradient: a modeling analysis

Using an original, validated, high-fidelity model of pulmonary physiology, we compared the arterial to end-tidal CO(2) gradient divided by the arterial CO(2) tension (Pa-E'CO(2)/PaCO(2)) with alveolar dead space expressed as a fraction of alveolar tidal volume, calculated in the conventional manner using Fowler's technique and the Bohr equation: (VDalv/VTalv)(Bohr-Fowler). We examined the variability of Pa-E'CO(2)/PaCO(2) and of (VDalv/VTalv)(Bohr-Fowler) in the presence of three ventilation-perfusion defects while varying CO(2) production (Vdot;CO(2)), venous admixture, and anatomical dead space fraction (VDanat). Pa-E'CO(2)/PaCO(2) was approximately 59.5% of (VDalv/VTalv)(Bohr-Fowler). During constant alveolar configuration, the factors examined (Vdot;CO(2), pulmonary shunt fraction, and VDanat) each caused variation in (VDalv/VTalv)(Bohr-Fowler) and in Pa-E'CO(2)/PaCO(2). Induced variation was slightly larger for Pa-E'CO(2)/PaCO(2) during changes in VDanat, but was similar during variation of venous admixture and Vdot;CO(2). Pa-E'CO(2)/PaCO(2) may be a useful serial measurement in the critically ill patient because all the necessary data are easily obtained and calculation is significantly simpler than for (VDalv/VTalv)(Bohr-Fowler).

IMPLICATIONS

Using an original, validated, high-fidelity model of pulmonary physiology, we have demonstrated that the arterial to end-tidal carbon dioxide pressure gradient may be used to robustly and accurately quantify alveolar dead space. After clinical validation, its use could replace that of conventionally calculated alveolar dead space fraction, particularly in the critically ill.